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Mathematics

Find the smallest 4-digit number which is exactly divisible by 32, 36 and 48.

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Answer

First, we find the LCM of 32, 36 and 48.

232, 36, 48
216, 18, 24
28, 9, 12
24, 9, 6
22, 9, 3
31, 9, 3
31, 3, 1
1, 1, 1

LCM of 32, 36 and 48 = 2 × 2 × 2 × 2 × 2 × 3 × 3 = 288.

The smallest 4-digit number is 1000.

We divide 1000 by 288 and find the remainder.

x213288)1000‾x+))−864‾x2+2136\begin{array}{l} \phantom{x^2 1}{\quad 3} \ 288\overline{\smash{\big)}1000} \ \phantom{x^ + )}\phantom{)}\underline{-864} \ \phantom{{x^2 } + 2} 136 \ \end{array}

The remainder is 136.

The required smallest 4-digit number = 1000 + (288 − 136) = 1000 + 152 = 1152.

Hence, the smallest 4-digit number divisible by 32, 36 and 48 is 1152.

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